Category Archives: Problem Solving

125. View from … Pensthorpe

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The Sandpit is currently in Norfolk and on a daytrip to Pensthorpe. In the ‘Wild Rootz’ adventure playground there is a bridge – except it’s not.

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It’s a damped ‘see-saw’, which you can run up and down. This is great fun – people run from one end to the other and try to reach the end before it goes down, with a bump.

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However, you can also use the principle of moments to try and balance the bridge. It took a bit of running up and down and fine tuning (bouncing), but we got the bridge balanced with five members of the family, age range: 84, weight range: wouldn’t be polite to say.

If you know somewhere near you, with a similar piece of equipment, this would be a brilliant way to demonstrate moments with a Sixth Form class. Obviously the calculations would be slightly out, due to the effect of the dampers, but it’s still fun – and a lot safer than piling a whole class on a see-saw.

122. Secret Lifeline

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How do you keep the pupils’ focussed on a peer’s explanation in a big classroom?

If a pupil is solving a problem on the board at the front, some of the class see this as an opportunity for low-level disruption. They often don’t see it as inappropriate behaviour and dealing with it can be off-putting for the pupil at the front. What to do?
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Equipment
A class set of named lolly sticks
Lolly sticks aren’t a new idea, but this is a different way to use them.

Activity
Set out the lolly sticks in teams face down on the desk, depending on the number of questions.
So an activity with 5 questions and 30 pupils would have 6 pupils per question. It doesn’t matter if the final team needs more pupils.

Set the first question. Give the class thinking time.

Randomly select a team by turning over one lolly stick. That person comes to the front to answer the question. The rest of the team are lifelines – if the team leader gets stuck, he/she can turn over a lifeline and ask for help. At the end of the question, the unused sticks remain face down.

Next question? Select the next team.

Why it works
No-one knows who will be called upon to contribute next, so everyone (who hasn’t yet contributed) must pay attention.

Hint
If your last team is short on lifelines, they can select any face down lolly stick.

I’ve used this with Y11 set 3/4 and it worked a treat, with everyone focussed on the task.

106. Musical Fractions

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Some unbelievers dispute it, but the truth is out there: Mathematics is everywhere!

The link between fractions and music is inescapable. If your notes don’t add up correctly, the music just doesn’t sound right. Crotchets, quavers, semi-breves, time signatures – it’s all maths.

Musical Fractions
I really like doing this activity with Year 7. Please make sure there are no tests or exams going on nearby.

Equipment
Mini-whiteboards
Percussion instruments (or clapping)
Earplugs (optional)

Aim
To introduce and practice adding simple unitary fractions.

Activity
Each type of musical note lasts for a specific amount of time. For example a crotchet lasts one beat. The picture below shows different notes and values:

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A dotted note lasts 50% longer than it normally would.

Time signatures tell you how many beats are in each bar of music (very simplified explanation). So:
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To make this into a lesson, ask students to create their own rhythms adding up to 3 or 4 beats.

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Start by doing 4 single beats by clapping or using instruments. This sounds like ‘tah, tah, tah, tah’ when you say it.

Then try some half notes – one, one, half, half, one. This sounds like ‘tah, tah, ta-te, tah’.

Throw in some quarter notes – one, half, half, quarter, quarter, quarter, quarter, one. This sounds like ‘tah, ta-te, tafi-tifi, tah’.

Now you can let the pupils loose to create their own rhythms using unitary fractions. You can get the pupils to write the fraction additions on their whiteboards. Each group can demonstrate their rhythm and teach it to the rest of the class.

I hope the ringing in your ears fades by the end of the day.

102. Can you stay out of the Boardroom?

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The_Apprentice__The_Final

The Apprentice regularly features its contestants failing to listen to what people want, often with disastrous results.

  •  They carry out market research with the wrong people or not enough people.
  • They assume the people they are asking are brilliant or thick. Seriously, you won’t find a world class wine expert working in the local supermarket!
  • They don’t change their product to meet the needs of the people.
  • Worse than that – they ignore the brief!

It all of this leads to one place: The Boardroom

Can your pupils avoid being fired?

I’ve been using ‘The Apprentice’ as an inspiration for a data handling project for years and I’ve finally typed up a resource to go with it.

Download Would Lord Sugar invest in you? worksheet

91. Scouting for Symmetry

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This week a relative joined the Scout Association in Wales. I knew that welsh scouts wore ‘Y Ddraig Goch’ (The Red Dragon or Welsh Flag) on their uniform. I didn’t know they wore it on each sleeve, symmetrically:

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This gave me the idea for a symmetry homework.

If you look at the uniformed services and uniformed youth movements, how often does symmetry occur in their badges? Do some badge styles occur in several associations? Are some images deliberately stylised to make them symmetrical? Are repeated emblems always placed symmetrically on either side of a uniform?

Pupils could also design their own symmetrical class reward badges.

From a pastoral point of view, this would be a nice way to celebrate younger pupils’ interests outside school.

88. Factor (Nasty) Game

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Today, it’s a classic maths game which has been passed around for at least 12 years, if not longer. It develops basic number skills such as multiplication, division, factors, primes, squares and place value.

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Equipment
A whiteboard (or wall or floor)
Ten digit cards (0-9): you could also just write the digits, but cards are more fun/tactile.
Blu-tak
Mini-whiteboards (or paper)
Calculators are optional

Before you start
You need between 2 and 5 teams. Five gives you more tension/excitement.

Each team needs a whiteboard.
Indicate on the board where each team puts their cards. They need tens and units columns.

Blu tak the number cards to the board.

Basic game
Each team takes it in turn to pick a card and place it in one of their columns. This is repeated so that every team has a two digit number. If you have five teams, there will be no leftover digits.

Winners
The winning team is the one whose number had the most factors. It is up to the teams to prove this by giving all the calculations of factors. Other teams may challenge their accuracy. You can also discuss why some numbers have an odd number of factors (eg square numbers) or exactly two factors (prime numbers).

Time to get Nasty
I said this game was called Factor Nasty … and it is.

There is only one change to the game rules: you can pick a digit and put it in any team’s answer box. They can use their number skills to really stitch each other up.

Imagine Team A puts a 0 in Team C’s tens column. Then Team B puts a 3 in Team C’s units column. Team C can’t do anything to improve their number, but they can make life tricky for Team A and B. Meanwhile, Teams D and E ignore them and create really good answers.

Have fun trying this as a starter or plenary!

86. Snapdragon & Resources

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I’ve just started sharing resources on the Times Educational Supplement (TES) website.

The first resource is a typed up version of the Trigonometry Snapdragon.
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I’ve omitted the diagrams so you can have a discussion about what the different situations look like.
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Update: I am hosting my own resources now so you can download the snapdragon here: Trigonometry snapdragon v2